Quantum entanglement and macroscopic quantum superpositions

Transcription

1 Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany Quantum entanglement and macroscopic quantum superpositions Johannes Kofler Quantum Information Symposium Institute of Science and Technology (IST) Austria 7 March 2013

2 Outlook Quantum entanglement vs. local realism Bell s inequality Loopholes Entanglement swapping & teleportation Macroscopic quantum superpositions vs. macrorealism Leggett-Garg inequality Quantum-to-classical transition Witnessing non-classical evolutions in complex systems Conclusion and outlook

3 Local realism Classical world view: Realism: properties of physical objects exist independent of whether or not they are observed by anyone Locality: no physical influence can propagate faster than the speed of light External world Passive observers

4 Bell s inequality Realism Locality Alice Bob Local realism: A = A(a,λ,b,B) outcomes A = ±1 B = ±1 B = B(b,λ,a,A) settings a 1,a 2 b 1,b 2 A 1 (B 1 +B 2 ) + A 2 (B 1 B 2 ) = ±2 λ variables S := A 1 B 1 + A 1 B 2 + A 2 B 1 A 2 B 2 2 Bell s inequality* Quantum mechanics: S QM = using entangled quantum states, e.g. Φ AB = ( HV AB + VH AB ) / 2 First experimental violation: 1972 Since then: tests with photons, atoms, superconducting qubits, *J. S. Bell, Phys. 1, 195 (1964); J. F. Clauser et al., PRL 23, 880 (1969)

5 Quantum entanglement Entangled state: Φ AB = ( HV AB + VH AB ) / 2 Picture:

6 Loopholes Loopholes: maintain local realism despite S exp > 2 Why important? - Quantum foundations - Security of entanglement-based quantum cryptography Three main loopholes: Locality loophole hidden communication between the parties closing: hard for atoms, achieved for photons (1982 1, ) Freedom of choice settings are correlated with hidden variables closing: hard for atoms, achieved for photons ( ) Fair sampling measured ensemble is not representative closing: achieved for atoms ( ) and photons ( ) E(λ) 1 A. Aspect et al., PRL 49, 1804 (1982) 2 G. Weihs et al., PRL 81, 5039 (1998) 3 T. Scheidl et al., PNAS 107, (2010) 4 M. A. Rowe et al., Nature 409, 791 (2001) 5 M. Giustina et al., Nature in print (2013)

7 Ensuring locality & freedom of choice Tenerife B,b La Palma E,A E(λ) a Locality: Alice s measurement event A is space-like separated from Bob s measurement event B and his setting choice b (and vice versa) Freedom of choice: Setting choices (a and b) are random and space-like separated from the entangled pair emission event E(λ): p(a,b λ) = p(a,b) T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, (2010)

8 Ensuring fair sampling Two main ingredients: Superconducting transition edge sensors Eberhard inequality* - undetected ( u ) events in derivation - required detection efficiency 66.7% From Topics in Applied Physics 99, (2005) +1 1 Source +1 1 Local realism J A B = Coo( α1, β1) Coo( α1, β2) Coo( α 2, β1) + Coo( α 2, β2) + So ( α1) + So ( β1) 0 *P. H. Eberhard, PRA 47, 747 (1993)

9 First fair sampling of photons J A B = Coo( α1, β1) Coo( α1, β2) Coo( α 2, β1) + Coo( α 2, β2) + So ( α1) + So ( β1) 0 Local realism Quantum violation of local realism with fair sampling Detection efficiency 75% Violation by 70 standard deviations Photon: only system for which all loopholes are closed; not yet simultaneously M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. K., Jörn Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, A. Zeilinger, Nature in print (2013)

10 Large distances How to distribute entanglement over large distances? - qu. cryptography between Vienna and Paris - distributed quantum computation Two answers: - glass fibers & quantum repeaters - no fibers: free space Quantum repeaters use entanglement swapping* Bell-state measurement (BSM): Entanglement swapping * M. Žukowski et al., PRL 71, 4287 (1993)

11 Delayed-choice entanglement swapping Later measurement on photons 2 & 3 decides whether 1 & 4 were separable or entangled Naïve class. interpretation would require influences into the past Temporal order does not matter in qu. mechanics X. Ma, S. Zotter, J. K., R. Ursin, T. Jennewein, Č. Brukner, A. Zeilinger, Nature Phys. 8, 479 (2012)

12 Quantum teleportation Towards a world-wide quantum internet X. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, A. Mech, B. Wittmann, J. K., E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, A. Zeilinger, Nature 489, 269 (2012)

13 Contents Quantum entanglement vs. local realism Bell s inequality Loopholes Entanglement swapping & teleportation Macroscopic quantum superpositions vs. macrorealism Leggett-Garg inequality Quantum-to-classical transition Witnessing non-classical evolutions in complex systems Conclusion

14 The double slit experiment Particles Waves Quanta Superposition: ψ = left + right Picture:

15 Macroscopic superpositions With photons, electrons, neutrons, molecules etc. With cats? cat left + cat right? 6910 AMU When and how do physical systems stop to behave quantum mechanically and begin to behave classically ( measurement problem )?

16 Local realism vs. macrorealism Are non-local correlations possible? Quantum mechanics says: yes (use entanglement) Local realism (e.g. classical physics) says no (only classical correlations) Bell test has given experimental answer in favor of quantum mechanics Practical relevance qu. computation, qu. cryptography Are macroscopic superpositions possible? Quantum mechanics says: yes (if you manage to defy decoherence) Macrorealism (e.g. classical physics, objective collapse models) says no (only classical temporal correlations) Leggett-Garg test can/will give experimental answer community still split Practical relevance witnessing temporal qu. coherence

17 Macrorealism Macrorealism per se: given a set of macroscopically distinct states, a macroscopic object is at any given time in a definite one of these states Non-invasive measurability: measurements reveal the state without any effect on the state itself or on the subsequent dynamics Leggett-Garg inequality (LGI) Bell: Quantum mechanics: K := Q 1 Q 2 + Q 2 Q 3 + Q 3 Q 4 Q 1 Q 4 2 = non-invasiveness S := A 1 B 1 + A 1 B 2 + A 2 B 1 A 2 B 2 2 = locality t 0 Q Q Q Q ±1 t 1 t 2 t 3 t 4 time K QM = A. J. Leggett and A. Garg, PRL 54, 857 (1985)

18 Quantum vs. classical Rotating spin ½ particle (eg. electron) Rotating classical spin vector (eg. gyroscope) ½ Precession around an axis (via magnetic field or external force) Measurments along different axis K > 2: violation of Leggett- Garg inequality K 2: no violation, classical time evolution 2 2 classical limit

19 Sharp vs. coarse-grained measurements Spin j Sharp measurement of spin z-component Coarse-grained measurement or decoherence Q = 1 j +j Q = +1 j +j macroscopically distinct states classical limit Violation of Leggett-Garg inequality for arbitrarily large spins j Classical physics of a rotating classical spin vector J. K. and Č. Brukner, PRL 99, (2007)

20 Superposition vs. mixture Sharp measurements Coarse-grained measurements or decoherence To see quantumness: need to resolve j 1/2 levels & protect system from environment J. K. and Č. Brukner, PRL 101, (2008)

21 Non-classical evolutions are complex Rotation in real space classical Oscillating Schrödinger cat non-classical rotation in Hilbert space N elementary spins ½ + + time t t t t time 1 single computation step per t all N rotations can be done simultaneously N sequential steps per t J. K. and Č. Brukner, PRL 101, (2008)

22 Relation quantum-classical

23 Macroscopic candidates Heavy molecules 1 (position) Superconducting devices 2 (current) Atomic gases 3 (spin) Nanomechanics 4 (position, momentum) 1 S. Gerlich et al., Nature Comm. 2, 263 (2011) 3 B. Julsgaard et al., Nature 413, 400 (2001) 2 M. W. Johnson et al., Nature 473, 194 (2011) 4 G. Cole et al., Nature Comm. 2, 231 (2011)

24 Alternative to Leggett-Garg inequality No-signaling in time (NSIT): A measurement does not change the outcome statistics of a later measurement. * t 0 A B t A t B MR NSIT Violation of NSIT witnesses non-classical time evolution Advantages of NSIT compared to LGI: - Only two measurement times (simpler witness) - Violated for broader parameter regime (better witness) LGI and NSIT are tools for witnessing temporal quantum coherence in complex systems (not necessarily having macroscopic superpositions) Does quantum coherence give biological systems an evolutionary advantage? * J. K. and Č. Brukner, arxiv: , to be published (2013)

25 Candidates for quantum biology Photosynthesis: Light harvesting in the FMO complex Avian compass electronic excitation (by sunlight) in antenna is transferred to reaction center evidence for efficiency increase due to quantum coherent transport radical pair mechanism proposed reaction products depend on earth magnetic field M. Sarovar et al., Nature Phys. 6, 462 (2010) N. Lambert et al., Nature Phys. 9, 10 (2013)

26 Conclusion and outlook Local realism - world view radically different from quantum mechanics - violated experimentally (Bell tests) by qu. entanglement - all loopholes are closed, but not yet simultaneously - loopholes relevant for qu. cryptography - long distance distribution of entanglement Macrorealism - related to the measurement problem (Schrödinger s cat) - quantum mechanics predicts violation - quantum-to-classical transition - Leggett-Garg inequality (LGI) not yet violated for macroscopic objects; several candidates - no-signaling in time (NSIT) as an alternative - LGI and NSIT: tools for witnessing quantum time evolution in mesoscopic systems including biological organisms

27 Acknowledgments Caslav Brukner Ignacio Cirac Anton Zeilinger Maximilan Ebner Marissa Giustina Thomas Herbst Thomas Jennewein Michael Keller Mateusz Kotyrba Xiao-song Ma Alexandra Mech Sven Ramelow Thomas Scheidl Mandip Singh Rupert Ursin Bernhard Wittmann Stefan Zotter